Question 73070
<pre>
Use the arthimetis sequence of numbers 1,3,5,7,9,... to find the following what is d, the difference between any 2 terms? show work 
 
              
        d = 3 - 1 
          = 2              

Using the formula for the nth term of an arthimetoc sequence, what is the 101st term? show work? 

{{{a[1] = 1}}}
   d = 2
   n = 101
            {{{a[n] = a[1] + (n - 1)d}}}
            {{{a[n] = 1 + (101 - 1)2}}}
            {{{a[n] = 1 + (100)2}}}
            {{{a[n] = 1 + 200}}}
            {{{a[n] = 201}}}

Using the formula for the sum of an arthimetic sequence, what is the sum of the first 20 terms? show work 

{{{a[1] = 1}}}
   d = 2
   n = 20
                    n
            {{{S[n]}}} = ___ {{{(a[1] + a[n])}}}
                    2
            
Let us find {{{a[n]}}} first: 
            {{{a[n] = a[1] + (n - 1)d}}}
            {{{a[n] = 1 + (20 - 1)2}}}
            {{{a[n] = 1 + (19)2}}}
            {{{a[n] = 1 + 38}}}
            {{{a[n] = 39}}}


                    20
            {{{S[n]}}} = ___ {{{(1 + 39)}}}
                    2

                         
            {{{S[n]}}} =  10 (40)
                       = 400                                   

            

Using the formula for the sum of an arthimetic sequence, what is the sum of the first 30 terms? show work

{{{a[1] = 1}}}
   d = 2
   n = 30
                    n
            {{{S[n]}}} = ___ {{{(a[1] + a[n])}}}
                    2
            
Let us find {{{a[n]}}} first: 
            {{{a[n] = a[1] + (n - 1)d}}}
            {{{a[n] = 1 + (30 - 1)2}}}
            {{{a[n] = 1 + (29)2}}}
            {{{a[n] = 1 + 58}}}
            {{{a[n] = 59}}}


                    30
            {{{S[n]}}} = ___ {{{(1 + 59)}}}
                    2

                         
            {{{S[n]}}} =  15 (60)
                       =  900